Update 2024-03-01-数学学习.md

_posts/2024-03-01-数学学习.md

@@ -178,5 +178,21 @@ $dx^x/dx = x^x (1 + ln x)$
 
 $\lim_{n \to \infty} (1 + \frac{1}{n})^n$ 为什么 = e
 
+ln 答案 = $ln(1 + 1/n)^n = n*ln(1+1/n)$
+
+设$\Delta x$ = 1/n -> 0
+
+= $1/\Delta x$ $ ln(1+\Delta x)$
+
+= $1/\Delta x$ $ln(1+\Delta x) - ln 1$
+
+可以看做d lnx / dx | x = 1
+
+因为ln x' = 1/x，所以d lnx / dx | x = 1结果为1
+
+ln 答案 = $ln(\lim_{n \to \infty} (1 + \frac{1}{n})^n)$ = 1
+
+答案 = $\lim_{n \to \infty} (1 + \frac{1}{n})^n = e^{ln(\lim_{n \to \infty} (1 + \frac{1}{n})^n)}$ = e
+